Binary Calculator
Enter two binary numbers (0s and 1s) and choose an operation. Results appear in binary, decimal and hexadecimal.
Binary Operations
Binary Result
How binary numbers work
Binary is the base-2 number system used by every digital device. It uses only two digits, 0 and 1, where each position is a power of 2. For example the binary number 1010 equals 1×8 + 0×4 + 1×2 + 0×1 = 10 in decimal.
Addition follows the same idea as decimal but carries at 2 instead of 10: 1 + 1 = 10 (write 0, carry 1). For example 101 + 11 = 1000, which is 8 in decimal.
Bitwise operations
AND, OR and XOR compare the numbers bit by bit. AND returns 1 only when both bits are 1; OR returns 1 when at least one bit is 1; XOR returns 1 when the bits differ.
NOT flips every bit of the number. Programmers use these operations for flags, masks and low-level data manipulation. The calculator treats inputs as unsigned 32-bit values, matching common programming behavior.
How to use this calculator
- Type binary number A (only 0s and 1s).
- Type binary number B for two-input operations.
- Choose the operation and press Calculate.
- Read the result in binary, decimal and hexadecimal.
Pro tips
- Add leading zeros to see matching bit widths, e.g. 0011 + 0001.
- Use AND with 1 to check whether the last bit is odd.
- XOR is useful for simple encryption and checksums.
Advantages & considerations
✅ Advantages
- Full arithmetic plus bitwise operations
- Shows decimal and hex for every result
- Divides with quotient and remainder
⚠️ Considerations
- Bitwise results use 32-bit unsigned representation
- Input is validated strictly as 0s and 1s